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  • 整体思路以及计算方式
  • 时间复杂度
  • 训练以及loss
  • 代码
  • 实验以及适用场景
  • 细节
  • 简评
  1. MHA
  2. SparseOrLowRank

Long-Short Transformer: Efficient Transformers for Language and Vision

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Last updated 2 years ago

论文地址：

参考资料：

整体思路以及计算方式

利用Local Attention计算局部Attention(short-term)，利用降维的方式计算全局Attention(long-term)，最终达到降低时间复杂度的效果。

short-term计算方式：

假设绿色部分长宽分别为l1,l2l_1, l_2l1​,l2​，那么总时间复杂度为O(l1l2d×n/l1)=O(nl2d)O(l_1l_2 d \times n/l_1)=O(nl_2 d)O(l1​l2​d×n/l1​)=O(nl2​d)

long-term计算方式：

  • 给定Q∈Rn×d,K,V∈Rm×dQ\in \mathbb R^{n\times d}, K,V\in \mathbb R^{m\times d}Q∈Rn×d,K,V∈Rm×d

  • Wp∈Rd×r,P=Softmax(KWp)∈Rm×rW^{p} \in \mathbb R^{d\times r},P=\mathrm{Softmax}( K W^p)\in \mathbb R^{m\times r}Wp∈Rd×r,P=Softmax(KWp)∈Rm×r

  • Kˉ=P⊤K∈Rr×d,Vˉ=P⊤V∈Rr×d\bar K = P^{\top} K \in \mathbb R^{r\times d}, \bar V = P^{\top} V \in \mathbb R^{r\times d}Kˉ=P⊤K∈Rr×d,Vˉ=P⊤V∈Rr×d

  • O=Softmax(QKˉ⊤)Vˉ∈Rn×dO=\mathrm{Softmax}(Q \bar K^{\top} ) \bar V \in \mathbb R^{n\times d}O=Softmax(QKˉ⊤)Vˉ∈Rn×d

总的时间复杂度为O((n+m)dr)O((n+m)dr)O((n+m)dr)。

融合：

  • 记short-term对应的K,VK, VK,V分别为K1,V1∈Rw×dK_1, V_1\in \mathbb R^{w\times d}K1​,V1​∈Rw×d

  • 记long-term对应的K,VK, VK,V分别为K2,V2∈Rr×dK_2, V_2\in \mathbb R^{r\times d}K2​,V2​∈Rr×d

  • O=Softmax(Q[LN1(K1):LN2(K2)]⊤)[LN1(V1):LN2(V2)]∈Rn×dO=\mathrm{Softmax}(Q [\mathrm{LN}_1(K_1): \mathrm{LN}_2(K_2)]^{\top} ) [\mathrm{LN}_1(V_1): \mathrm{LN}_2(V_2)] \in \mathbb R^{n\times d}O=Softmax(Q[LN1​(K1​):LN2​(K2​)]⊤)[LN1​(V1​):LN2​(V2​)]∈Rn×d

总时间复杂度为O(n(r+w)d)O(n(r+w)d)O(n(r+w)d)。

时间复杂度

总时间复杂度为O(n(r+w)d)O(n(r+w)d)O(n(r+w)d)。

训练以及loss

不变。

代码

实验以及适用场景

测试了lra, lm以及imagenet，效果都很好。

细节

单向模型中还有一些实现细节。

简评

效果挺好的，但是整体方法感觉不算优雅，一些实现细节可以参考。

https://github.com/NVIDIA/transformer-ls
https://arxiv.org/abs/2107.02192
https://blog.csdn.net/qq_43542339/article/details/118771339